Title: Sequential pattern generation with modular threshold-linear networks
Abstract: Neural circuits in the brain perform a variety of essential functions, including input classification, pattern completion, and the generation of rhythms that support functions such as breathing and locomotion. Traditionally, rhythmic activity has been modeled using coupled oscillators, whereas persistent activity has been modeled using attractor neural networks. In this talk, I use combinatorial threshold-linear networks (CTLNs) to demonstrate that a single network can produce static patterns, dynamic patterns, and combinations of both. First, I will present a modular network construction that can generate combinatorially many limit cycles. This relies on a theorem for CTLNs that decomposes the fixed points of a composite network into those of its component subnetworks. Using this theorem, we can build a single network that robustly encodes five distinct quadruped gaits (bound, pace, trot, walk, and pronk) as coexisting attractors, without requiring parameter changes, and where transitions between gaits are possible via simple external pulses. I will also present an extension of this theorem to a broader family of networks (generalized CTLNs). And second, I will introduce a network that can step through a prescribed sequence of gaits. This is achieved by connecting the quadruped gait network to a “counter” network that tracks external inputs via a sequence of stable fixed points. This construction fuses the dynamic attractors from the quadruped gaits network with the static attractors of the counter network. The modular nature of the network allows it to flexibly reuse existing patterns in different combinations with no interference between patterns.